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In fact, El-Erian’s colleague Bill Gross told CNBC that "I don't think the Fed is vigilant in terms of the negative aspects of zero-bound rates. I don't think they're vigilant in terms of other central banks and their quantitative easing policies. I don't think they're vigilant in terms of asset prices."

"One of the problems that the Fed has had over the past 10 years is that they have not focused on asset prices," Gross (right) emphasized.

The network notes that he argued the Fed’s focus on unemployment and inflation—which he acknowledged has been vigilant—was "almost to the asset price exclusion," causing it to miss the 2008 housing bubble and "the destruction that asset prices can wreak upon an economy, in addition to higher inflation."

St. Louis Fed President James Bullard, who appeared with Gross, naturally took issue with his comments, according to CNBC.

"I think we are [vigilant]," he said. "We take all those aspects into account."

The Fed has better systems in place to track financial markets, Bullard said, adding, "We certainly talk to the other central banks. We are well aware of what they're doing."

Bullard continued, "[The] systems in place on tracking what's going on, making sure that we're at least aware of different aspects of financial markets ... those systems are a lot better than they were five years ago. And we are trying to have better market intelligence."

Gross later told Bloomberg Television that quantitative easing would continue to "at least the end of the year."

Gross said that the Federal Reserve knew that its policy had negatives: "The chairman recognizes that," he said.

He also spoke about returning to the gold standard, which would be "very difficult."